U.S. Trade Representative William E. Brock yesterday predicted a "further deterioration" in America's trade deficit with Japan but said a turn-around could take place in 1984.

"The situation will get worse before it gets better," the Reagan administration's top trade official said at a breakfast with reporters the day after Japanese Prime Minister Yasuhiro Nakasone left Washington. The question of trade dominated Nakasone's three days of talks with administration officials, including two meetings with President Reagan.

Brock was pessimistic about any quick fixes for the United States' growing trade imbalance with Japan, but he cautioned against following the protectionist route which is being pushed by many labor and business leaders and which has strong support in Congress.

"Protectionism is not the right response because it hurts us more that anyone else," said Brock, who added that is the advice he will give to Congress.

"This is going to be a very, very difficult year, almost regardless of what happens in specific trade actions because this protectionist momentum now has built to such a degree that it is not going to turn around fast, any more than the trade situation is going to turn around fast."

The first of what is expected to be a series of trade hearings by various committees in the Senate and House is scheduled for Wednesday, when Brock will be a chief witness before the Senate Finance Committee.

Brock said the 1982 trade deficit with Japan amounted to about $18 billion and is expected to grow to $20 billion to $24 billion this year. This amounts to between 35 percent and 40 percent of America's total trade deficit, he said.

Even if the Nakasone government takes all the steps toward opening its markets that the Reagan administration wants, Brock said it will take time before they begin to show up in increased sales of American goods in Japan. That, along with the continued strength of the dollar against an unnaturally weak yen, could postpone any turnaround in the United States' trade deficit with Japan.

Meanwhile, Brock said he will hold talks in Tokyo next month on an extension of an agreement that for the past two years has limited U.S. imports of Japanese autos.

Brock hinted he will suggest the voluntary restraints be extended for another two years because, if they are not, he said, the question will come up again in the middle of the 1984 election campaign.

"My own instincts," he said, "are relatively strong that there would be a lot of pressure in 1984 to extend the agreement for a fourth year and that is a tough time to consider a question like that."

The political implications of the trade issue were demonstrated by Brock himself in November, when he called for an extension of the restraints in a letter to Sen. John C. Danforth (R-Mo.). Danforth was caught in a tough race against a labor-supported candidate and used Brock's letter to show his support for American autoworkers.

While the Japanese have not responded officially, Nakasone's Minister of International Trade and Industry Sadanori Yamanaka suggested the limits may not be extended if the U.S. auto market improves. Other Japanese officials said the limits may be extended but the number of cars shipped to the United States increased from the present quota of 1.68 million a year.